Problem: Rewrite the function by completing the square. $f(x)=x^{2}+16x-46$ $f(x)=(x+$
Explanation: We want to complete $x^2{+16}x$ into a perfect square. To do that, we should add $\left(\dfrac{{+16}}{2}\right)^2={64}$ to it: $x^2{+16}x+{64}=(x+8)^2$ In order to keep the expression equivalent, we add and subtract ${64}$, not forgetting the expression's constant term, $-46$ : $\begin{aligned} f(x)&=x^2+16x-46 \\\\ &=x^2+16x+{64}-46-{64} \\\\ &=(x+8)^2-46-64 \\\\ &=(x+8)^2-110 \end{aligned}$ In conclusion, after completing the square, the function is written as $f(x)=(x + 8)^2 - 110$